Use Lagrange Multipliers to Find the Maximum Value of the Function

question 121

Short Answer

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.
$$f ( x , y ) = 8 x ^ { 2 } - 4 y ^ { 2 } , 8 x ^ { 2 } + 4 y ^ { 2 } = 8$$

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Definitions:

Inventory Turnover

A ratio showing how many times a company's inventory is sold and replaced over a period, indicating the efficiency of inventory management and sales performance.

Cost of Goods Sold

The direct costs attributable to the production of the goods sold by a company, including materials and labor costs.

Period

A length of time in financial reporting, often quarterly or annually, used to evaluate business performance.

Cost of Goods Manufactured

The total cost incurred by a company to produce goods in a specific period, including labor, material, and overhead costs.